Effect of surface roughness on the anomalous heat conductance at solid/superfluid helium interfaces: a way of quantifying phonon scattering in microstructures

Abstract

Heat transfer mechanisms at very small length scales are studied at the boundary between solid and superfluid helium-4 (He II) at temperatures of 1–2 K. We shall show that this configuration is interesting and may prove useful in future heat conduction analysis in microstructures and across film/substrate boundaries. We define two possible heat conduction regimes, namely a classical surface effect regime and a scattering effect regime for the solid/He II system. The distinction between these regimes depends upon the (l/λ) ratio, where the surface roughness extent is l at a given length scale and the phonon wavelength is λ. We analyse our results of heat conduction across solid–superfluid helium interfaces and we show that the conductance can be entirely explained by the scattering effect regime where diffuse phonon scattering from surface irregularities of nanometric scale lengths play a dominant role. We also provide evidence of the existence of a frequency dependence of the heat transmission coefficient and, we compare the heat conduction with that in microstructures.